What is the Catholic Church's position on the scientific theory of evolution?

Question

Understanding the scientific [Biological] theory of evolution simply as descent [from a common ancestor] with modification through Darwin's proposed mechanism of natural selection, starting from the time Darwin published the Origin of Species in 1859, what is the Catholic Church's position on the scientific theory of evolution as expressed through papal magisterium?

What is/is not acceptable for a Catholic as regards this theory?

What are the proscribed limits set forth by the papal magisterium?

From the papal teaching, why is the theory of evolution of interest to the Church?

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Science as understood in

Science is a particular way of knowing about the world. In science, explanations are limited to those based on observations and experiments that can be substantiated by other scientists. Science is not the only way of acquiring knowledge about ourselves and the world around us. Humans gain understanding in many other ways, such as through literature, the arts, philosophical reflection, and religious experience. Scientific knowledge may enrich aesthetic and moral perceptions, but these subjects extend beyond science's realm, which is to obtain a better understanding of the natural world. Explanations that cannot be based on empirical evidence are not part of science. - Source: 1999 report "Science and Creationism: A View from the National Academy of Sciences, Second Edition"

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^{Please note that this question is not asking about Theistic Evolution, a non-scientific theory.}

Answer 1

A quick Google search provides a link indicating there is (perhaps intentionally) no official authoritative declaration on the subject, leaving "no burden upon conscience".

To quote,

[The advantage of Catholics] lies in the simple fact that they do not have to decide either for Evolution or against it. Authority has not spoken on the subject; hence it puts no burden upon conscience, and may be discussed realistically and without prejudice. A certain wariness, of course, is necessary. I say that authority has not spoken; it may, however, speak tomorrow, and so the prudent man remembers his step. But in the meanwhile there is nothing to prevent him examining all available facts, and even offering arguments in support of them or against them—so long as those arguments are not presented as dogma. (STJ, 163)

And, again, referencing Pope Pius in the 1950s,

In other words, the Pope could live with evolution, so long as the process of “ensouling” humans was left to God. (He also insisted on a role for Adam, whom he believed committed a sin— mysteriously passed along through the “doctrine of original sin”—that has affected all subsequent generations.) Pius XII cautioned, however, that he considered the jury still out on the question of evolution’s validity. It should not be accepted, without more evidence, “as though it were a certain proven doctrine.” (ROA, 81)

Answer 2

In his 22 October 1996 Address to the Plenary Session on the Subject ‘The Origins and Early Evolution of Life’ Pope St. John Paul II [the Great] said , 'he wanted to remind [those addressed] that the Magisterium of the Church has already made pronouncements on these matters within the framework of her own competence.' The Pope went on to cite two interventions. One of those was from Pope Pius XII in his Encyclical Humani Generis (1950). The Pope said

In his Encyclical Humani Generis (1950), my predecessor Pius XII had already stated that there was no opposition between evolution and the doctrine of the faith about man and his vocation, on condition that one did not lose sight of several indisputable points.[Cf. AAS 42 (1950), pp. 575-576.]

Therefore the Magisterium of Pope Pius XII sets conditions on the theory of evolution based on several indisputable points. Some of those points are

1. [...] [The] Teaching Authority of the Church does not forbid that, in conformity with the present state of human sciences and sacred theology, research and discussions, on the part of men experienced in both fields, take place with regard to the doctrine of evolution, in as far as it inquires into the origin of the human body as coming from pre-existent and living matter - for the Catholic faith obliges us to hold that souls are immediately created by God.
2. However, this must be done in such a way that the reasons for both opinions, that is, those favorable and those unfavorable to evolution, be weighed and judged with the necessary seriousness, moderation and measure, and
3. [Provided] that all are prepared to submit to the judgment of the Church, to whom Christ has given the mission of interpreting authentically the Sacred Scriptures and of defending the dogmas of faith.
4. Some however, rashly transgress this liberty of discussion, when they act as if the origin of the human body from pre-existing and living matter were already completely certain and proved by the facts which have been discovered up to now and by reasoning on those facts, and as if there were nothing in the sources of divine revelation which demands the greatest moderation and caution in this question. - Source: Pope Pius XII Encyclical Humani Generis (1950), 36.

From above, it is clear that the Church does not take a position for or against evolution; opposing opinions are to be given due consideration; allows for scientific research to continue, and allows for discussions between expert scientists and experts in sacred theology; limits the inquiry to the origin of the human body only - the Catholic Faith puts the soul off-limits; what is not certain should not be taken as such and what has not been proven should not be taken as a fact; conclusions cannot contradict divine revelation; because of her divine-given mission of interpreting authentically the Sacred Scriptures and of defending the dogmas of faith, the Church can step in at anytime and pronounce a judgment that must be assented to by all the faithful.

One other limit that the Church imposes on her children is that they do not have the liberty to embrace the conjectural opinion of polygenism.

The other Magisterium that Pope St. John Paul II [the Great] says must be taken into account is the Conciliar Constitution Gaudium et Spes which magnificently explained this doctrine: 'Revelation teaches us that he [man] was created in the image and likeness of God.'

For the OP's final question, the saintly Pope says

The Church’s Magisterium is directly concerned with the question of evolution, for it involves the conception of man[.]

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Please see: Papal Addresses to the Pontifical Academy of Sciences 1917-2002 and to the Pontifical Academy of Social Sciences 1994-2002.

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Needless to say, based on the understanding of the scientific [Biological] theory of evolution simply as descent [from a common ancestor] with modification through Darwin's proposed mechanism of natural selection, the OP does not see a reconciliation of the theory from the scientific perspective with the limits the Church has imposed. To illustrate, since the soul is beyond what science can measure, the scientist would want to conclude that the whole man, body and soul, evolved in accordance with the theory of evolution.